introduction to using r

An Introduction to R

Graeme L. Hickey

31st October 2014

Graeme L. Hickey An Introduction to R 31st October 2014 1 / 125

Getting ready to use R

Logistics

Owing to room change, there will unfortunately be less hands-onexperience (possibly none)I will email the slides to all who registered – no need to make notesWe will take a short break during

What is R?

Derives from a proprietary software packaged called S-Plus

“R is a free software programming language and softwareenvironment for statistical computing and graphics” Wikipedia(2014)

The “lingua franca of data analysts” The New York Times(2009)

Used worldwide by bioinformaticians, data scientists, high-level statisticians,app developers, . . .

Why use R?

Keep whole analysis together (data processing, analysis, publicationfigures, reports)Reproducible researchState of the art statistical methods are wrapped up in ‘R packages’It’s freeIt’s cross platform (Windows, OSX, Linux) compatibleIt will be extensively used in EPH / IGH statistical training

Objectives

The primary objective is for you to be able to apply statisticalfunctions available in R to your own data

To achieve this we should be able to:

Understand the core concepts of R and its syntaxBe able to read and write data filesBe able to interrogate a datasetBe able to use functions and optionsBe able to write a simple function

How to install R?

Download and install from: http://www.r-project.orgCan use in isolation, but combing with an IDE front-end makes lifeeasier when starting outRecommend using R Studio: http://www.rstudio.comOnce both programs installed, only ever need to run R Studio

R Studio

R Console vs. Script Editor

Would you consider writing your thesis using a typewriter?

Don’t just use the console – not reproducible!Always write analysis as an R ScriptFile -> New File -> R ScriptHighlight code and press Ctrl + Enter to execute

R as a calculator

Simple maths

## [1] 3

13 * 17

## [1] 221

((6 * 7) + 4 - 7) / 2^8

## [1] 0.1523438

R as a calculator

Routine mathematical functions and constants

exp(3)

## [1] 20.08554

sin(2 * pi) - 1

## [1] -1

atan(1) ^ 2

## [1] 0.6168503

All of these examples use base R functions – we’ll revisit these laterGraeme L. Hickey An Introduction to R 31st October 2014 12 / 125

R as a calculator

Other ‘numbers’ to look out for

## [1] Inf

-1 / 0

## [1] -Inf

## [1] NaN

If you see these, you have probably done something wrong!Graeme L. Hickey An Introduction to R 31st October 2014 13 / 125

Data objects

Assignment operator

We can tell R to remember things so that we can call them laterWe do this using either assignment operators = or <-

x <- 5x

## [1] 5

x = 5x

## [1] 5

Data objects

A warning!

R is case SENSITIVE

This is a common error and can lead to a great deal of pain in tracing bugs!

x # Lowercase

## [1] 5

X # Uppercase

## Error in eval(expr, envir, enclos): object 'X' not found

Data objects

Another warning!

Names cannot begin with numbers or include spaces

gra.eme_30 <- 5 # OK30graeme <- 5 # Not allowed!gra eme <- 5 # Not allowed either!

Data objects

What do you think the following lines of R code will output at the end?

x <- 2y <- piz <- (sin(y) + x)^2z

Try it!

Data objects

Solution

x <- 2y <- piz <- (sin(y) + x)^2z

## [1] 4

Data objects

x <- 2x <- x + 5x

Try it!

Data objects

Solution

x <- 2x <- x + 5x

## [1] 7

Data objects

Vectors

We often have more than a single number, which we combine into avector using the function, e.g.

c(184, 162, 145, 200, 178, 154, 172, 142)

## [1] 184 162 145 200 178 154 172 142

heights <- c(184, 162, 145, 200, 178, 154, 172, 142)heights

## [1] 184 162 145 200 178 154 172 142

Data objects

heights/10 + 1

Try it!

Data objects

Solution

heights/10 + 1

## [1] 19.4 17.2 15.5 21.0 18.8 16.4 18.2 15.2

Data objects

Selection

We might want to select the 5-th value from a vectorWe use square brackets for this, e.g.

heights[5]

## [1] 178

Data objects

heights[c(1, 3, 5)]

Try it!

Data objects

Solution

heights[c(1, 3, 5)]

## [1] 184 145 178

Data objects

Boils down to something being TRUE or FALSE

x > y asks: is x greater than y?x < y asks: is x less than y?

x == y asks: is x equal to y?x >= y asks: is x greater than or equal to y?x <= y asks: is x less than or equal to y?

Data objects

Basic examples

5 < 10

## [1] TRUE

## [1] FALSE

sin(pi) == cos(pi) + 1

## [1] FALSE

Data objects

We can combine logical statements, for example

(5 < 10) & (3 < 5)

## [1] TRUE

(1 > 2) | (3 > 4)

## [1] FALSE

Data objects

Logic & selection

We can use a logical vector to pick out elements of a vector so long as thelogical vector and the vector of data are the same length

logic.vec <- c(TRUE, FALSE, TRUE, FALSE, TRUE,FALSE, TRUE, FALSE)

heights[logic.vec]

## [1] 184 145 178 172

Task: How do you extract heights greater than 160cm?

Data objects

SolutionHow to extract heights greater than 160cm?

i <- (heights > 160)i

## [1] TRUE TRUE FALSE TRUE TRUE FALSE TRUE FALSE

heights[i]

## [1] 184 162 200 178 172

And once you understand, simply. . .

heights[heights > 160]

## [1] 184 162 200 178 172Graeme L. Hickey An Introduction to R 31st October 2014 32 / 125

Data objects

Character data

Vectors don’t just store numbersThey can store items of class: integer, numeric, character, date,factor, etc.For character data, just put things inside quotation marks

subjects <- c("Bob", "Amy", "Amy", "Bob", "Amy","Bob", "Bob", "Amy", "Amy")

subjects

## [1] "Bob" "Amy" "Amy" "Bob" "Amy" "Bob" "Bob" "Amy" "Amy"

Data objects

MatricesThese are generalizations of vectors: instead of being one vector, we havemultiple columns of vectors:

matrix(heights, nrow = 2)

## [,1] [,2] [,3] [,4]## [1,] 184 145 178 172## [2,] 162 200 154 142

matrix(subjects, nrow = 3)

## [,1] [,2] [,3]## [1,] "Bob" "Bob" "Bob"## [2,] "Amy" "Amy" "Amy"## [3,] "Amy" "Bob" "Amy"

Data objects

MatricesWe can apply the same arithmetic as per vectors

myMat <- matrix(heights, nrow = 2)myMat

## [,1] [,2] [,3] [,4]## [1,] 184 145 178 172## [2,] 162 200 154 142

0.5*myMat + 3

## [,1] [,2] [,3] [,4]## [1,] 95 75.5 92 89## [2,] 84 103.0 80 74

Data objects

Matrices

Each row and column has to have data of the same type (e.g. numeric,character, logical) — you can’t mix-and-matchMost useful when do linear algebra (e.g. PCA, solve systems ofequations)R often coerces into matrix form when required by functionsIf you want different data types, need to use objects calleddata.frames

Data objects

Data frames

Think of these like Microsoft Excel spreadsheetsColumns represent different variables, e.g. age, sex, number of cells,. . .Rows represent samples, e.g. patients, testsLike matrices, they are a generalization of vectors, but can storedifferent types of data

Data objects

Data frames

R has some pre-installed data frames, including the infamous Sir RonaldFisher iris dataset1, to allow us to practice

## Sepal.Length Sepal.Width Petal.Length Petal.Width Species## 1 5.1 3.5 1.4 0.2 setosa## 2 4.9 3.0 1.4 0.2 setosa## 3 4.7 3.2 1.3 0.2 setosa## 4 4.6 3.1 1.5 0.2 setosa## 5 5.0 3.6 1.4 0.2 setosa

1R. A. Fisher (1936). The use of multiple measurements in taxonomic problems.Annals of Eugenics 7 (2): 179–188.

Data objects

Selection in data frames

Earlier, we learnt how to select individual elements from a vectorFor a data frame the same principles apply, except there are now 2dimensions: rows and columns (note the order!)

Data objects

Selection in data frames

There are 3 primary methods of selecting data from data frames

1 Square brackets2 Using the dollar ($) operator (for columns only)3 Using the subset function (we won’t discuss this today)

They all do the same thing (sort of), and you can combine these methods

Data objects

Selection using square brackets

One method of selection is the square brackets:

dat[i , ] would select the i-th row (which is a vector)dat[ , j] would select the j-th column (which is a vector)dat[i, j] would select the value from the i-th row and j-th column

Data objects

iris[1, 1]

## [1] 5.1

iris[ , 1]

## [1] 5.1 4.9 4.7 4.6 5.0 5.4 4.6 5.0 4.4 4.9 5.4 4.8 4.8## [14] 4.3 5.8 5.7 5.4 5.1 5.7 5.1 5.4 5.1 4.6 5.1 4.8 5.0## [27] 5.0 5.2 5.2 4.7 4.8 5.4 5.2 5.5 4.9 5.0 5.5 4.9 4.4## [40] 5.1 5.0 4.5 4.4 5.0 5.1 4.8 5.1 4.6 5.3 5.0 7.0 6.4## [53] 6.9 5.5 6.5 5.7 6.3 4.9 6.6 5.2 5.0 5.9 6.0 6.1 5.6## [66] 6.7 5.6 5.8 6.2 5.6 5.9 6.1 6.3 6.1 6.4 6.6 6.8 6.7## [79] 6.0 5.7 5.5 5.5 5.8 6.0 5.4 6.0 6.7 6.3 5.6 5.5 5.5## [92] 6.1 5.8 5.0 5.6 5.7 5.7 6.2 5.1 5.7 6.3 5.8 7.1 6.3## [105] 6.5 7.6 4.9 7.3 6.7 7.2 6.5 6.4 6.8 5.7 5.8 6.4 6.5## [118] 7.7 7.7 6.0 6.9 5.6 7.7 6.3 6.7 7.2 6.2 6.1 6.4 7.2## [131] 7.4 7.9 6.4 6.3 6.1 7.7 6.3 6.4 6.0 6.9 6.7 6.9 5.8## [144] 6.8 6.7 6.7 6.3 6.5 6.2 5.9

Data objects

Selection using square brackets

i and j don’t have to be single numbers, they can be:

vectors of numberslogical vectors (which need to be the same length as the rows orcolumns)

iris[c(1, 3) , ]

## Sepal.Length Sepal.Width Petal.Length Petal.Width Species## 1 5.1 3.5 1.4 0.2 setosa## 3 4.7 3.2 1.3 0.2 setosa

Data objects

Selection using the dollar operator

Each column in a data frame should have a nameWe use dat$foo1 to extract the column called foo1 from a dataframe called dat, e.g.

iris$Petal.Width

## [1] 0.2 0.2 0.2 0.2 0.2 0.4 0.3 0.2 0.2 0.1 0.2 0.2 0.1## [14] 0.1 0.2 0.4 0.4 0.3 0.3 0.3 0.2 0.4 0.2 0.5 0.2 0.2## [27] 0.4 0.2 0.2 0.2 0.2 0.4 0.1 0.2 0.2 0.2 0.2 0.1 0.2## [40] 0.2 0.3 0.3 0.2 0.6 0.4 0.3 0.2 0.2 0.2 0.2 1.4 1.5## [53] 1.5 1.3 1.5 1.3 1.6 1.0 1.3 1.4 1.0 1.5 1.0 1.4 1.3## [66] 1.4 1.5 1.0 1.5 1.1 1.8 1.3 1.5 1.2 1.3 1.4 1.4 1.7## [79] 1.5 1.0 1.1 1.0 1.2 1.6 1.5 1.6 1.5 1.3 1.3 1.3 1.2## [92] 1.4 1.2 1.0 1.3 1.2 1.3 1.3 1.1 1.3 2.5 1.9 2.1 1.8## [105] 2.2 2.1 1.7 1.8 1.8 2.5 2.0 1.9 2.1 2.0 2.4 2.3 1.8## [118] 2.2 2.3 1.5 2.3 2.0 2.0 1.8 2.1 1.8 1.8 1.8 2.1 1.6## [131] 1.9 2.0 2.2 1.5 1.4 2.3 2.4 1.8 1.8 2.1 2.4 2.3 1.9## [144] 2.3 2.5 2.3 1.9 2.0 2.3 1.8

Data objects

1 Select all rows of the iris data where the sepal length is >7.6cm2 Extract the sepal lengths of iris flowers sp. virginica with petal widths

>2.4cm

N.B. there are multiple ways of solving these problems

Data objects

Solution (1)

iris[iris$Sepal.Length > 7.6, ]

## Sepal.Length Sepal.Width Petal.Length Petal.Width## 118 7.7 3.8 6.7 2.2## 119 7.7 2.6 6.9 2.3## 123 7.7 2.8 6.7 2.0## 132 7.9 3.8 6.4 2.0## 136 7.7 3.0 6.1 2.3## Species## 118 virginica## 119 virginica## 123 virginica## 132 virginica## 136 virginica

Data objects

Solution (2)I’ll break this one into pieces to make it clearer. . .lvec1 <- (iris$Petal.Width > 2.4)lvec2 <- (iris$Species == "virginica")iris2 <- iris[lvec1 & lvec2, ]iris2

## Sepal.Length Sepal.Width Petal.Length Petal.Width## 101 6.3 3.3 6.0 2.5## 110 7.2 3.6 6.1 2.5## 145 6.7 3.3 5.7 2.5## Species## 101 virginica## 110 virginica## 145 virginica

iris2$Sepal.Length

## [1] 6.3 7.2 6.7

Data objects

I could have combined all of this into a single line. . .

iris[(iris$Petal.Width > 2.4) &(iris$Species == "virginica"), ]$Sepal.Length

## [1] 6.3 7.2 6.7

Data objects

Factors

An important class of data in R are factorsThey are categorical variables, e.g. gender, countryThey are similar to character data, except that R is “aware” of them,which allows us to do lots of clever things with our data

Data objects

iris$Species

## [1] setosa setosa setosa setosa setosa## [6] setosa setosa setosa setosa setosa## [11] setosa setosa setosa setosa setosa## [16] setosa setosa setosa setosa setosa## [21] setosa setosa setosa setosa setosa## [26] setosa setosa setosa setosa setosa## [31] setosa setosa setosa setosa setosa## [36] setosa setosa setosa setosa setosa## [41] setosa setosa setosa setosa setosa## [46] setosa setosa setosa setosa setosa## [51] versicolor versicolor versicolor versicolor versicolor## [56] versicolor versicolor versicolor versicolor versicolor## [61] versicolor versicolor versicolor versicolor versicolor## [66] versicolor versicolor versicolor versicolor versicolor## [71] versicolor versicolor versicolor versicolor versicolor## [76] versicolor versicolor versicolor versicolor versicolor## [81] versicolor versicolor versicolor versicolor versicolor## [86] versicolor versicolor versicolor versicolor versicolor## [91] versicolor versicolor versicolor versicolor versicolor## [96] versicolor versicolor versicolor versicolor versicolor## [101] virginica virginica virginica virginica virginica## [106] virginica virginica virginica virginica virginica## [111] virginica virginica virginica virginica virginica## [116] virginica virginica virginica virginica virginica## [121] virginica virginica virginica virginica virginica## [126] virginica virginica virginica virginica virginica## [131] virginica virginica virginica virginica virginica## [136] virginica virginica virginica virginica virginica## [141] virginica virginica virginica virginica virginica## [146] virginica virginica virginica virginica virginica## Levels: setosa versicolor virginica

Data objects

Matrices and data frames too limited?

What if you need something more than a flat matrix or data.frame?E.g. recording 100 measurements for 70 subjects at 25 time points?array and ?list

Functions

What are functions?

In short, you put something in and get something outIn order to do interesting things with out data and apply the wealth ofstatistical methods available, we need to understand about functionsfirst

Functions

Recognising a function

Functions must have an assigned nameFunctions are applied using round bracketsFunctions generally take arguments (either required or optional)Arguments can be anything, depending on the function, but often oneof them will be some data

e.g. myFunc(x)

Functions

Base R functions

R has lots of built in functions, which you can apply to most data objects

Functions

summary

summary(iris)

## Sepal.Length Sepal.Width Petal.Length## Min. :4.300 Min. :2.000 Min. :1.000## 1st Qu.:5.100 1st Qu.:2.800 1st Qu.:1.600## Median :5.800 Median :3.000 Median :4.350## Mean :5.843 Mean :3.057 Mean :3.758## 3rd Qu.:6.400 3rd Qu.:3.300 3rd Qu.:5.100## Max. :7.900 Max. :4.400 Max. :6.900## Petal.Width Species## Min. :0.100 setosa :50## 1st Qu.:0.300 versicolor:50## Median :1.300 virginica :50## Mean :1.199## 3rd Qu.:1.800## Max. :2.500

Functions

head & tail

If you want to inspect a data frame, you don’t want to look at thewhole thingWe use either the head() or tail() functionsOr if using R Studio, click the Environment tab

head(iris)

## Sepal.Length Sepal.Width Petal.Length Petal.Width Species## 1 5.1 3.5 1.4 0.2 setosa## 2 4.9 3.0 1.4 0.2 setosa## 3 4.7 3.2 1.3 0.2 setosa## 4 4.6 3.1 1.5 0.2 setosa## 5 5.0 3.6 1.4 0.2 setosa## 6 5.4 3.9 1.7 0.4 setosa

Functions

ncol, nrow, dim

ncol(iris)

## [1] 5

nrow(iris)

## [1] 150

dim(iris)

## [1] 150 5

Functions

length

dim() doesn’t work on vectors, so we have to use length()

length(heights)

## [1] 8

Functions

names(iris)

## [1] "Sepal.Length" "Sepal.Width" "Petal.Length"## [4] "Petal.Width" "Species"

Functions

Mathematical functions

We saw some of these before, e.g.

sin(pi) # Not zero as R is using numerical approximation

## [1] 1.224647e-16

exp(pi*4)

## [1] 286751.3

Functions

Statistical functions

mean(heights)

## [1] 167.125

sd(heights)

## [1] 20.09575

range(heights)

## [1] 142 200

Functions

Warnings & Errors

Sometimes we get messages listed as Warning and Error

Warnings mean that the function was able to do something, but what itreturns may not be what you were expecting

Errors mean that the function aborted as something did not makesense

Don’t ignore either unless you are 100% confident why ithappened!

Functions

mean(iris)

## Warning in mean.default(iris): argument is not numeric or## logical: returning NA

## [1] NA

sin(Pi)

## Error in eval(expr, envir, enclos): object 'Pi' not found

Functions

1 How many iris samples have petal widths >2cm?2 Of these, what is the mean and SD of their petal lengths?

Functions

Solutions

x <- iris[iris$Petal.Width > 2, ]nrow(x)

## [1] 23

mean(x$Petal.Length)

## [1] 5.76087

sd(x$Petal.Length)

## [1] 0.4793358

Functions

Some functions take multiple arguments and it is often best to formallydeclare them, e.g.

seq(from = 1, to = 10, by = 2)

## [1] 1 3 5 7 9

But if confident of the order, we could just apply

seq(1, 10, 2)

## [1] 1 3 5 7 9

Functions

Shorthand trick

We can replace the function seq(x, y, by = 1) with x:y, e.g.

seq(1, 10, 1)

## [1] 1 2 3 4 5 6 7 8 9 10

Functions

Making a data frame from vectorsIf we have vectors v1, v2, v3, then we can make our own data frame usingthe data.frame function

ID <- seq(1, 8, 1)heights.m <- heights / 10 # Heights in metresdata.frame(ID, heights, heights.m)

## ID heights heights.m## 1 1 184 18.4## 2 2 162 16.2## 3 3 145 14.5## 4 4 200 20.0## 5 5 178 17.8## 6 6 154 15.4## 7 7 172 17.2## 8 8 142 14.2

Functions

Coercion

We can coerce one data type into another using the as.* functions, e.g.

as.data.frame()as.matrix()as.vector()as.numeric()

Don’t worry about these for now, but handy for your own studies one day

Functions

Merging 2 (or more) data frames

If you have 2 data frames, that share a common field, e.g. subject IDs,we can merge them together using merge()This is particularly useful for longitudinal datasets

Functions

Let’s make another data set

Species <- c("setosa", "versicolor", "virginica")Colours <- c("red", "blue", "violet")flowerCols <- data.frame(Species, Colours)flowerCols

## Species Colours## 1 setosa red## 2 versicolor blue## 3 virginica violet

Functions

Now let’s merge them

irisMerge <- merge(iris, flowerCols)head(irisMerge, 5)

## Species Sepal.Length Sepal.Width Petal.Length Petal.Width## 1 setosa 5.1 3.5 1.4 0.2## 2 setosa 4.9 3.0 1.4 0.2## 3 setosa 4.7 3.2 1.3 0.2## 4 setosa 4.6 3.1 1.5 0.2## 5 setosa 5.0 3.6 1.4 0.2## Colours## 1 red## 2 red## 3 red## 4 red## 5 red

Functions

Writing our own function

We can write our own functions when neededWe use the function() functionWe must remember to assign it to a name, otherwise we can’t use it

myFun <- function(arguments) {# do something

Functions

E.g. f (x) = ex + x2 + 1

fx <- function(x) {exp(x) + x^2 + 1

}fx(5)

## [1] 174.4132

fx(seq(3, 12, 3))

## [1] 30.08554 440.42879 8185.08393 162899.79142

Functions

Comments

Notice that anything written after a hash-symbol is ignored by RUse this to annotate your R scripts to remember what you are doing

# Graeme thinks R is great!# R will ignore all of this

Functions

Help with functions

There are thousands of functions in RSome are loaded on launch of R (e.g. mean, seq, dim)Others require packages to be loaded firstIf you know the name of a function, you can use the ? operator toaccess the help file, e.g.

Functions

Help with functions

You can also use the search bar in the R Studio softwareIf you don’t know the name of the function, try the help.search fora list of possible candidates

help.search("sequences")

When all else fails: Google it!

Conditional statements and loops

Introduction

Inherent to all programming languages are conditional statementsand loopsRequire them when we need to make complex rulesWould require a more advanced tutorial to fully appreciate the powerIf interested to learn more, see references at end

Conditional statements

The if statement, which is technically a function, only does something ifTRUE, e.g.

if(3 < 4) {3 + 3}

## [1] 6

if(3 > 4) {2 + 2}

Also, look up while and else using help.search()

We might want to sequentially do something, conditional on somethingelseFor example, let Yi = Yi−1 + i/10 with Y1 = 0Calculate Y =

∑20i=1 Yi

E.g. 0 + (0 + 2/10) + (2/10 + 3/10) + . . . + (2/10 + 3/10 + . . .+ 20/10)

Y <- 0 # Start with Y_1for(i in 2:20) {

Yi <- Y + i/10 # Calculate Y_iY <- Y + Yi # Cummulative sum

}Y # Solution

## [1] 157284.2

For each value in our heights vector earlier, how can we calculate thedifference between it and the previous one, i.e. calculate heightsi -heightsi−1?

Solution

d <- 0for(i in 2:length(heights)) {

d[i] <- heights[i] - heights[i-1]}d

## [1] 0 -22 -17 55 -22 -24 18 -30

Reading and writing files

Reading

You want to get your data into RData comes in lots of different formats, luckily R can handle almost allof them!Most use packages – we’ll explore these later

read.csv

The simplest way is to convert your data to a comma separated value(*.csv) files and use

my.data <- read.csv(file.choose())

Instead of writing file.choose() we could have specified the filelocationLook at the help file for more customization settings

read.xlsx

Converting our data to CSV format is a pain!We can use the xlsx package instead

library("xlsx")my.data <- read.xlsx(file.choose(), sheetIndex = 1)

foreign

What if our data is in a Stata, SPSS, SAS, etc. file?We can use the foreign package instead, e.g.

library("foreign")my.data <- read.spss(file.choose())

Data on the web

What if our data is in the cloud?We can use the utils package function download.file instead, e.g.

library("utils")my.data <- download.file("http://www.liv.ac.uk/dat.csv")

Useful if you share your data on a public Dropbox folder

Other formats

If data exists, R can read it inJust need to find the right package

Writing

Usually as simple as change the read. to write.

Need to specify:

1 What file we want to save2 A name for the file we will save

write.csv(iris, "IrisData.csv")

Graphics

Introduction

R has 3 primary graphics packages2:

1 Base R - those built into R2 lattice - a functional extensional of the base graphics (requires a

package)3 ggplot2 - built on the grammar of graphics (requires a package)

All called using functions, and typically have lots of optional arguments forcustomization of figures

2I will discuss packages shortly.Graeme L. Hickey An Introduction to R 31st October 2014 96 / 125

Graphics

The plot function can be applied to most data objects

Alternatively, one can give it two arguments:

x - x-axis coordinatesy - y-axis coordinates

Can also specify arguments to: label the axes; colour the points; etc. See:?help

Graphics

plot(iris)

Sepal.Length

2.0 2.5 3.0 3.5 4.0 0.5 1.0 1.5 2.0 2.5

Sepal.Width

Petal.Length

Petal.Width

4.5 5.5 6.5 7.5 1 2 3 4 5 6 7 1.0 1.5 2.0 2.5 3.0

Species

Graphics

How can I plot the sepal length against the petal length of the iris data, andcolour the points by species?

Hint: ?as.numeric + ?plot

Graphics

Solution

plot(x = iris$Sepal.Length, y = iris$Petal.Length,col = as.numeric(iris$Species))

4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0

iris$Sepal.Length

Graphics

Histograms

hist(iris$Petal.Length,col = "grey", xlab = "Petal length (cm)")

Histogram of iris$Petal.Length

Petal length (cm)

1 2 3 4 5 6 7

Graphics

Boxplots

boxplot(Petal.Length ~ Species, data = iris)

setosa versicolor virginica

Graphics

ggplot2

Flexible publication quality graphics

library("ggplot2")

Graphics

ggplot(aes(x = Petal.Length, y = Petal.Width, colour = Sepal.Length),data = iris) +

geom_point() + geom_smooth() +facet_wrap(~ Species, scales = "free")

setosa versicolor virginica

1.00 1.25 1.50 1.75 3.0 3.5 4.0 4.5 5.0 4.5 5.0 5.5 6.0 6.5 7.0Petal.Length

Sepal.Length

Graphics

Saving figures

In R Studio, click Export then select file typeIn R, right click + Save

Packages

Introduction

Packages are like appsMany state of the art statistical methods published in journals with RpackagesLarge number of books released with specific R packages also,e.g. time series, prognostic modelling, survival regression, . . .Packages are published:

On CRANGit HubBio-conductorCode files on personal websites (not really packages per se)

Packages

Where to find relevant packages

There are thousands of R packages!Books, journal articles (look what is reported in the Statistical Analysissection), word of mouth, your local friendly statisticianwww.rseek.org

Packages

What packages are already installed?

R comes with a number of packages pre-installedWe can see all them, plus any we have installed ourselves

library() # No arguments!

or click the Packages tab if working from R Studio

Packages

Installing a package from CRAN

Once you have identified the package you want, run:

install.packages("ggplot2")

Packages

Loading a package

R does not automatically load all installed packages as it slows yourcomputer down, and can also cause clashes

When you know what package(s) you want to use, run:

library("ggplot2") # Load ggplot2 package

Statistics

Introduction

In R, statistical method is just another term for functionBeware of applying statistical methods to your data withoutunderstanding what they do first: G-I-G-O!

Statistics

Student’s t-test

t.test(x = heights, mu = 180)

#### One Sample t-test#### data: heights## t = -1.8121, df = 7, p-value = 0.1129## alternative hypothesis: true mean is not equal to 180## 95 percent confidence interval:## 150.3245 183.9255## sample estimates:## mean of x## 167.125

Statistics

Notice that we applied a function to two arguments:

1 Some data2 A number

And it gave us back out some statistics and a P-value

Statistics

Linear regression

The first argument of many statistical functions is a formula

A formula is written as:

The outcome variable on the RHS (one of the variables in your dataset)A tilde symbol (~) which means model ontoThe explanatory variables on the RHS (separated by a + if more thanone)

Statistics

fit <- lm(Petal.Width ~ Sepal.Length, data = iris)fit

#### Call:## lm(formula = Petal.Width ~ Sepal.Length, data = iris)#### Coefficients:## (Intercept) Sepal.Length## -3.2002 0.7529

Statistics

Recall we can apply the summary function to different things?We have just assigned our linear model to the name fit

summary(fit)

#### Call:## lm(formula = Petal.Width ~ Sepal.Length, data = iris)#### Residuals:## Min 1Q Median 3Q Max## -0.96671 -0.35936 -0.01787 0.28388 1.23329#### Coefficients:## Estimate Std. Error t value Pr(>|t|)## (Intercept) -3.20022 0.25689 -12.46 <2e-16 ***## Sepal.Length 0.75292 0.04353 17.30 <2e-16 ***## ---## Signif. codes:## 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#### Residual standard error: 0.44 on 148 degrees of freedom## Multiple R-squared: 0.669, Adjusted R-squared: 0.6668## F-statistic: 299.2 on 1 and 148 DF, p-value: < 2.2e-16

Statistics

We can apply other functions to fit also, e.g.

plot(fit)

0.0 0.5 1.0 1.5 2.0 2.5

Fitted values

Residuals vs Fitted

115107

−2 −1 0 1 2

Theoretical Quantiles

Normal Q−Q

115107

0.0 0.5 1.0 1.5 2.0 2.5

Fitted values

Scale−Location115107

0 50 100 150

Obs. number

Cook's distance132

Statistics

Probability

Most routine statistical distributions are built-in, e.g. Gaussian (norm),Binomial (binom), Poisson (pois), . . .

We use a prefix:

d to get the densityp to get the cumulative probability distributionq to get the quantile functionr to sample random values from the distribution

Statistics

# Sample 5 values from a N(2, 9) distributionrnorm(5, mean = 2, sd = 3)

## [1] -2.370804 3.118035 -2.090598 2.051935 3.879390

# Probability of tossing 10 heads in a rowpbinom(0, size = 10, prob = 0.5)

## [1] 0.0009765625

Wrapping up

Saving your workspace

You can save everything you have done using File -> Save (R Studiowill prompt you when exiting)I never save my workspaceWhy? Because I save the R Script (copy & paste)

Wrapping up

Where to learn more

Venables WN, Smith DM (2014). An Introduction to R:http://cran.r-project.org/doc/manuals/R-intro.pdfShahbaba B (2012). Biostatistics with R. Springer, NY.Data Camp online course: https://www.datacamp.com/courses/Ask me, Peter, Elisabeth or Helen!

Wrapping up

Further IGH Statistical Seminars

Other sessions in this series will make use of R

Introduction to Time Series (5th Dec 2014)Regression Modelling (Jan 2015)Time-to-Event Analysis (Feb 2015)Geostatistical Methods for Disease Prevalence Mapping (March 2015)Statistical Power + Sample Size Calculations (April 2015)Quantile Regression (May 2015)

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base r functions

core concepts of r

rgetting ready

data filesbe able

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data processing

optionsbe able

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